Road Network Vulnerability Analysis Based on Improved Ant Colony Algorithm

Table 3

Utility and vulnerability of arcs at different capacity degradation.

Capacity degradation level		Arc 1	Arc 2	Arc 3	Arc 4	Arc 5
Normal	𝑥𝑎	7.152	12.072	4.776	7.152	4.776
	𝑐𝑎	1.004	2.208	1.103	1.203	1.104
	𝑒𝑎	0.577	0.065	0.631	0.622	0.600
10%	𝑥𝑎	7.752	10.968	5.280	7.752	5.280
	𝑐𝑎	1.009	2.216	1.106	1.207	1.109
	𝑒𝑎	0.396	0.046	0.442	0.440	0.411
	𝑉𝑎	0.313	0.293	0.300	0.292	0.315
20%	𝑥𝑎	8.328	9.960	5.712	8.328	5.712
	𝑐𝑎	1.020	2.236	1.114	1.215	1.119
	𝑒𝑎	0.243	0.024	0.285	0.286	0.255
	𝑉𝑎	0.578	0.625	0.549	0.540	0.575
30%	𝑥𝑎	8.832	9.072	6.096	8.832	6.096
	𝑐𝑎	1.043	2.277	1.131	1.233	1.143
	𝑒𝑎	0.121	0.001	0.157	0.160	0.129
	𝑉𝑎	0.790	0.980	0.751	0.742	0.784
40%	𝑥𝑎	9.264	8.352	6.384	9.264	6.384
	𝑐𝑎	1.095	2.368	1.169	1.273	1.195
	𝑒𝑎	0.030	−0.022	0.061	0.064	0.038
	𝑉𝑎	0.948	1.333	0.903	0.898	0.937
50%	𝑥𝑎	9.552	7.848	6.600	9.552	6.600
	𝑐𝑎	1.223	2.595	1.264	1.372	1.326
	𝑒𝑎	−0.025	−0.040	−0.003	−0.001	−0.021
	𝑉𝑎	1.044	1.618	1.005	1.002	1.035